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Polytope of Type {52,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,6}*624a
Also Known As : {52,6|2}. if this polytope has another name.
Group : SmallGroup(624,179)
Rank : 3
Schlafli Type : {52,6}
Number of vertices, edges, etc : 52, 156, 6
Order of s0s1s2 : 156
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {52,6,2} of size 1248
   {52,6,3} of size 1872
Vertex Figure Of :
   {2,52,6} of size 1248
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {26,6}*312
   3-fold quotients : {52,2}*208
   6-fold quotients : {26,2}*104
   12-fold quotients : {13,2}*52
   13-fold quotients : {4,6}*48a
   26-fold quotients : {2,6}*24
   39-fold quotients : {4,2}*16
   52-fold quotients : {2,3}*12
   78-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {104,6}*1248, {52,12}*1248
   3-fold covers : {52,18}*1872a, {156,6}*1872a, {156,6}*1872b
Permutation Representation (GAP) :
s0 := (  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)
( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)
( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)( 80,130)( 81,129)( 82,128)
( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)( 88,122)( 89,121)( 90,120)
( 91,119)( 92,131)( 93,143)( 94,142)( 95,141)( 96,140)( 97,139)( 98,138)
( 99,137)(100,136)(101,135)(102,134)(103,133)(104,132)(105,144)(106,156)
(107,155)(108,154)(109,153)(110,152)(111,151)(112,150)(113,149)(114,148)
(115,147)(116,146)(117,145);;
s1 := (  1, 80)(  2, 79)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)(  8, 86)
(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14,106)( 15,105)( 16,117)
( 17,116)( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)( 24,109)
( 25,108)( 26,107)( 27, 93)( 28, 92)( 29,104)( 30,103)( 31,102)( 32,101)
( 33,100)( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)( 40,119)
( 41,118)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)( 48,124)
( 49,123)( 50,122)( 51,121)( 52,120)( 53,145)( 54,144)( 55,156)( 56,155)
( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)
( 65,146)( 66,132)( 67,131)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)
( 73,138)( 74,137)( 75,136)( 76,135)( 77,134)( 78,133);;
s2 := (  1, 14)(  2, 15)(  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)(  8, 21)
(  9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)( 42, 55)
( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)
( 51, 64)( 52, 65)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)
( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)
(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)
(127,140)(128,141)(129,142)(130,143);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(156)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)
( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)( 80,130)( 81,129)
( 82,128)( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)( 88,122)( 89,121)
( 90,120)( 91,119)( 92,131)( 93,143)( 94,142)( 95,141)( 96,140)( 97,139)
( 98,138)( 99,137)(100,136)(101,135)(102,134)(103,133)(104,132)(105,144)
(106,156)(107,155)(108,154)(109,153)(110,152)(111,151)(112,150)(113,149)
(114,148)(115,147)(116,146)(117,145);
s1 := Sym(156)!(  1, 80)(  2, 79)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)
(  8, 86)(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14,106)( 15,105)
( 16,117)( 17,116)( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)
( 24,109)( 25,108)( 26,107)( 27, 93)( 28, 92)( 29,104)( 30,103)( 31,102)
( 32,101)( 33,100)( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)
( 40,119)( 41,118)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)
( 48,124)( 49,123)( 50,122)( 51,121)( 52,120)( 53,145)( 54,144)( 55,156)
( 56,155)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)
( 64,147)( 65,146)( 66,132)( 67,131)( 68,143)( 69,142)( 70,141)( 71,140)
( 72,139)( 73,138)( 74,137)( 75,136)( 76,135)( 77,134)( 78,133);
s2 := Sym(156)!(  1, 14)(  2, 15)(  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)
(  8, 21)(  9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)
( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)
( 50, 63)( 51, 64)( 52, 65)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)
( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)
(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)
(126,139)(127,140)(128,141)(129,142)(130,143);
poly := sub<Sym(156)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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